The present invention relates, in general, to optical metrology, and, in particular, to interferometric displacement measurement independent of the optical path length effects of the refractive index of a gas in a measurement path, including the effects of refractive index fluctuations.
A frequently encountered problem in precision interferometric metrology is the need to have accurate knowledge about the refractive index of a gas in a measurement path and/or the change in optical path length of the measurement path due to the gas. This is especially true where the refractive index of the gas may be fluctuating, e.g. the gas is turbulent, and/or the physical length of the measuring path may be changing. With accurate information about the index and its effects on changes in the optical path, it is possible to correct for errors caused by such effects in the determination of physical displacements in length and angle.
Several techniques exist for measuring the index under highly controlled circumstances, such as when an air column is contained in a sample cell and is monitored for temperature, pressure, and physical dimension. However, measuring index under uncontrolled conditions is technically challenging, particularly where high accuracies are required. Perhaps the most difficult measurement related to the refractive index of air is the measurement of refractive index fluctuations over a measurement path of unknown or variable length, with uncontrolled temperature and pressure. Such circumstances arise frequently in high-precision distance measuring interferometry, such as is employed in micro-lithographic fabrication of integrated circuits. See for example an article entitled "Residual errors in laser interferometry from air turbulence and non-linearity," by N. Bobroff, Appl. Opt. 26(13), 2676-2682 (1987), and an article entitled "Recent advances in displacement measuring interferometry," also by N. Bobroff, Measurement Science & Tech. 4 (9), 907-926 (1993).
As is known, interferometric displacement measurements in air are subject to environmental uncertainties, particularly to changes in air pressure and temperature; to uncertainties in air composition such as resulting from changes in humidity; and to the effects of turbulence in the air. Such factors alter the wavelength of the light used to measure the displacement.
Under normal conditions, the refractive index of air is approximately 1.0003 with a variation of the order of 1.times.10.sup.-5 to 1.times.10.sup.-4. However, in many applications the refractive index of air must be known with a relative precision of less than 0.1 ppm (parts per million) to 0.003 ppm, these two relative precisions corresponding to a displacement measurement accuracy of 100 nm and 3 nm, respectively, for a one meter interferometric displacement measurement.
One way to detect refractive index fluctuations is to measure changes in pressure and temperature along a measurement path and calculate the effect on the optical path length of the measurement path. Mathematical equations for effecting this calculation are disclosed in an article entitled "The Refractivity Of Air," by F. E. Jones, J. Res. NBS 86(1), 27-32 (1981). An implementation of the technique is described in an article entitled "High-Accuracy Displacement Interferometry In Air," by W. T. Estler, Appl. Opt. 24(6), 808-815 (1985). Unfortunately, this technique provides only approximate values, is cumbersome, and corrects only for slow, global fluctuations in air density.
Another, more direct way to detect the effects of a fluctuating refractive index over a measurement path is by multiple-wavelength distance measurement. The basic principle may be understood as follows. Interferometers and laser radar measure the optical path length between a reference and an object, most often in open air. The optical path length is the integrated product of the refractive index and the physical path traversed by a measurement beam. In that the refractive index varies with wavelength, but the physical path is independent of wavelength, it is generally possible to determine the physical path length from the optical path length, particularly the contributions of fluctuations in refractive index, provided that the instrument employs at least two wavelengths and the intrinsic optical properties of the gas are knowable. Since the variation of refractive index with wavelength is known in the art as dispersion, this technique is often referred to as the dispersion technique.
The dispersion technique for refractive index measurement has a long history in optical interference phase detection for shorter distances. In U.S. Pat. No. 3,647,302 issued in 1972 to R. B. Zipin and J. T. Zalusky, entitled "Apparatus For And Method Of Obtaining Precision Dimensional Measurements," there is disclosed an interferometric displacement-measuring system employing multiple wavelengths to compensate for variations in ambient conditions such as temperature, pressure, and humidity. The instrument is specifically designed for operation with a movable object, that is, with a variable physical path length. However, the phase-detection means of Zipin and Zalusky appears to be insufficiently accurate for high-precision measurement.
A recent attempt at high-precision interferometry for micro-lithography is represented by U.S. Pat. No. 4,948,254 issued to A. Ishida (1990). A similar device is described by Ishida in an article entitled "Two Wavelength Displacement-Measuring Interferometer Using Second-Harmonic Light To Eliminate Air-Turbulence-Induced Errors," Jpn. J. Appl. Phys. 28(3), L473-475 (1989). In the article, a displacement-measuring interferometer is disclosed which eliminates errors caused by fluctuations in the refractive index by means of two-wavelength dispersion detection.
In U.S. Pat. No. 5,404,222 entitled "Interferometric Measuring System With Air Turbulence Compensation," issued to S. A. Lis (1995), there is disclosed a two-wavelength interferometer employing the dispersion technique for detecting and compensating refractive index fluctuations. A similar device is described by Lis in an article entitled "An Air Turbulence Compensated Interferometer For IC Manufacturing," SPIE 2440 (1995). However, both Ishida and Lis rely on externally supplied data about the value of the reciprocal dispersive power of the gas occupying the measurement path.
It is clear from the foregoing, that the prior art does not provide a practical, high-speed, high-precision method and corresponding means for measuring refractive index of air and measuring and compensating for the optical path length effects of the air in a measuring path, particularly the effects due to fluctuations in the refractive index of the air. The limitations in the prior art arise principally from the following, unresolved technical difficulties: (1) Prior-art heterodyne and superheterodyne interferometers are limited in accuracy by fluctuations in the refractive index of air; (2) Prior-art dispersion techniques for measuring index fluctuations require extremely high accuracy in interference phase measurement, typically exceeding by an order of magnitude the typical accuracy of high-precision distance-measuring interferometers; (3) Obvious modifications to prior-art interferometers to improve phase-measuring accuracy would increase the measurement time to an extent incompatible with the rapidity of stage motion in modern micro-lithography equipment; (4) Prior-art dispersion techniques require at least two extremely stable laser sources, or a single source emitting multiple, phase-locked wavelengths; (5) Prior-art dispersion techniques in micro-lithography applications are sensitive to stage motion during the measurement, resulting in systematic errors; and (6) Prior-art dispersion techniques that employ doubling crystals (e.g. U.S. Pat. No. 5,404,222 to Lis) as part of the detection system are expensive and complicated.
These deficiencies in the prior art have led to the absence of any practical interferometric system for performing displacement measurement for micro-lithography in the presence of a gas in a measurement path where there are typically refractive index fluctuations and the measurement path is comprised of a changing physical length.
Accordingly, it is an object of the invention to provide a displacement measuring interferometric system by which the refractive index of a gas in a measurement path and/or the optical path length effects of the gas are rapidly and accurately measured and monitored wherein the refractive index may be fluctuating and/or the physical length of the measurement path may be changing.
It is another object of the invention to provide a displacement measuring interferometric system and method by which the refractive index of a gas in a measurement path and/or the optical path length effects of the gas are rapidly and accurately measured and monitored wherein the accuracy of measurements and monitoring of the refractive index of the gas and/or of the optical path length effects of the gas are substantially not compromised by a rapid change in physical length of measurement path.
It is another object of the invention to provide a displacement interferometric system and method by which the refractive index of a gas in a measurement path and/or the optical path length effects of the gas are rapidly and accurately measured and monitored wherein the system and method does not require measurement and monitoring of environmental conditions such as temperature and pressure.
It is another object of the invention to provide a displacement measuring interferometric system and method by which the refractive index of a gas in a measurement path and/or the optical path length effects of the gas are rapidly and accurately measured and monitored wherein the system and may, but does not require, use of two or more optical beams of differing wavelengths which are phase locked.
It is another object of the invention to provide displacement measuring interferometric systems and methods by which the refractive index of a gas in the measurement path and/or the optical path length effects of the gas are rapidly and accurately measured, monitored and used to accurately determine physical displacement by compensating for refractive index effects in the measurement path.
It is another object of the invention to provide displacement measuring interferometric systems and methods by which changes in the refractive index of a gas in the measurement path and/or the optical path length effects of the gas are accurately measured, monitored and used to accurately determine physical displacement by compensating for refractive index effects in the measurement path.
Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter. The invention accordingly comprises methods and apparatus possessing the construction, steps, combination of elements, and arrangement of parts exemplified in the detailed description to follow when read in connection with the drawings.